Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.     

The impact of human activity patterns on asymptomatic infectious processes in complex networks

The study of the impact of human activity patterns on network dynamics has attracted a lot of attention in recent years. However, individuals’ knowledge of their own physical states has rarely been incorporated into modeling processes. In real life, for certain infectious processes, infected agents may not have any visible or physical signs and symptoms; therefore, they may believe that they are uninfected even when they have been infected asymptomatically. This infection awareness factor is covered neither in the classical epidemic models such as SIS nor in network propagation studies. In this article, we propose a novel infectious process model that differentiates between the infection awareness states and the physical states of individuals and extend the SIS model to deal with both asymptomatic infection characteristics and human activity patterns. With regards to the latter, we focus particularly on individuals’ testing action, which is to determine whether an individual is infected by an epidemic. The simulation results show that less effort is required in controlling the disease when the transmission probability is either very small or large enough and that Poisson activity patterns are more effective than heavy-tailed patterns in controlling and eliminating asymptomatic infectious diseases due to the long-tail characteristic.     

Epidemic spreading on networks with vaccination

In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.     

Epidemic spreading in complex networks

The study of epidemic spreading in complex networks is currently a hot topic and a large body of results have been achieved. In this paper, we briefly review our contributions to this field, which includes the underlying mechanism of rumor propagation, the epidemic spreading in community networks, the influence of varying topology, and the influence of mobility of agents. Also, some future directions are pointed out.      

Epidemic spreading in scale-free networks

The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and persistence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.     

Naming game on small-world networks with geographical effects

The naming game model characterizes the main evolutionary features of languages or more generally of communication systems. Very recently, the combination of complex networks and the naming game has received much attention and the influences of various topological properties on the corresponding dynamical behavior have been widely studied. In this paper, we investigate the naming game on small-world geographical networks. The small-world geographical networks are constructed by randomly adding links to two-dimensional regular lattices, and it is found that the convergence time is a nonmonotonic function of the geographical distance of randomly added shortcuts. This phenomenon indicates that, although a long geographical distance of the added shortcuts favors consensus achievement, too long a geographical distance of the added shortcuts inhibits the convergence process, making it even slower than the moderates.     

Epidemic outbreaks in growing scale-free networks with local structure

The class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in BA model. Most of these models assume that only one node per time step joins the network. In this paper, we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment. This successfully generates key features observed in social networks. These include power-law degree distribution p_k∼k^−(3+μ), where μ=(n−1)/m is a tuning parameter defined as the modularity strength of the network, nontrivial clustering, assortative mixing, and modular structure. Moreover, all these features are dependent in a similar way on the parameter μ. We then study the susceptible-infected epidemics on this network with identical infectivity, and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure, especially the modularity strength. The modularity of the network makes the spreading velocity much lower than that of the BA model. On the other hand, increasing the modularity strength will accelerate the propagation velocity.     

Epidemic spreading with nonlinear infectivity in weighted scale-free networks

In this paper, we investigate the epidemic spreading for the SIR model in weighted scale-free networks with the nonlinear infectivity and weighted transmission rate. Concretely, we introduce the infectivity exponent α and the weight exponent β into the epidemic system, then examine the impact of α and β on the epidemic spreading. We show that one can adjust the values of α and β to rebuild a nonzero finite epidemic threshold. Furthermore, we also find the infectivity exponent α has a stronger effect not only on the epidemic threshold, but also on the epidemic prevalence. In addition, it is also interesting to see that the absence of the epidemic threshold appears not very dejected, since the prevalence grows much more slowly as the transmission rate λ increases.     

考虑网络流量的无标度网络病毒免疫策略研究

考虑网络交通流量对病毒传播行为的影响,基于平均场理论研究无标度网络上的病毒免疫策略,提出一种改进的熟人免疫机理.理论分析表明,在考虑网络交通流量影响的情况下,当免疫节点密度较小时,随机免疫几乎不能降低病毒的传播速率,而对网络实施目标免疫则能够有效抑制病毒的传播,并且选择度最大的节点进行免疫与选择介数最大的节点进行免疫的效果基本相同.研究还发现,对于网络全局信息未知的情况,与经典熟人免疫策略相比,所提出的免疫策略能够获得更好的免疫效果.通过数值仿真对理论分析进行了验证. 关键词： 无标度网络 病毒传播 交通流量 免疫策略     

Epidemic spreading on networks with overlapping community structure

Many real networks are characterized by overlapping community structures in which vertices may belong to more than one community. In this paper, we propose a network model with overlapping community structure. The analytical and numerical results show that the connectivity distribution of this network follows a power law. We employ this network to investigate the impact of overlapping community structure on susceptible-infected-susceptible (SIS) epidemic spreading process. The simulation results indicate that significant overlapping community structure results in a major infection prevalence and leads to a peak of the spread velocity in the early stages of the emerging infection.     

Epidemic outbreaks in complex heterogeneous networks

We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures. Received 20 September 2001 and Received in final form 4 February 2002     

Epidemic spreading in lattice-embedded scale-free networks

We study geographical effects on the spread of diseases in lattice-embedded scale-free networks. The geographical structure is represented by the connecting probability of two nodes that is related to the Euclidean distance between them in the lattice. By studying the standard susceptible-infected model, we found that the geographical structure has great influences on the temporal behavior of epidemic outbreaks and the propagation in the underlying network: the more geographically constrained the network is, the more smoothly the epidemic spreads, which is different from the clearly hierarchical dynamics that the infection pervades the networks in a progressive cascade across smaller-degree classes in Barabási–Albert scale-free networks.     

基于交通流量的病毒扩散动力学研究

不同于经典扩散模型中节点传染力等同于节点度k的假定, 基于交通流量的病毒扩散模型中, 各个节点的传染力可以等同于节点实际介数b_k. 利用平均场近似方法, 提出基于交通流量SIS病毒修正扩散模型. 根据修正SIS模型, 以最小搜索信息路由为例, 重新研究病毒传播率β, 平均发包率λ同传播阈值β_c, 平稳状态病毒密度ρ之间的关系. 理论分析与实验结果均表明, 当网络拓扑和路由策略一定时, 传播阈值β_c为实际介数b_k的均值<b_k>与其平方的均值<b_k²>的比值. 而稳定状态时感染密度ρ同感染同病毒传播率β, 平均发包率λ 以及λ =1时节点实际介数的均值<b_λ=1> 的乘积倒数存在幂率关系.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.     

Chimera states in networks of logistic maps with hierarchical connectivities

Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.     

Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission

We investigate the combinational effects of non-uniform transmission of edges and the network structure in susceptible-infected-removed models of the epidemic spreading. Here the degree-degree correlation is neglected and the transmission of individual edge depends on the degree of infected node. With the additional assumption that we can compartment a independent factor λ₀ from the transmission, we analyzed the effects of degree distribution P(k) and transmission distribution λ(k) on the threshold of λ₀.     

Epidemic threshold and phase transition in scale-free networks with asymmetric infection

We study the SIS epidemic dynamics on scale-freeweighted networks with asymmetric infection, by both analysis andnumerical simulations, with focus on the epidemic threshold aswell as critical behaviors. It is demonstrated that the asymmetryof infection plays an important role: we could redistribute theasymmetry to balance the degree heterogeneity of the network andthen to restore the epidemic threshold to a fnite value. On theother hand, we show that the absence of the epidemic threshold isnot so bad as commented previously since the prevalence grows veryslowly in this case and one could only protect a few vertices toprevent the diseases propagation.     

Detect overlapping and hierarchical community structure in networks

Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two properties of community structure separately. This paper proposes an algorithm (EAGLE) to detect both the overlapping and hierarchical properties of complex community structure together. This algorithm deals with the set of maximal cliques and adopts an agglomerative framework. The quality function of modularity is extended to evaluate the goodness of a cover. The examples of application to real world networks give excellent results.     

Epidemic spreading on random surfer networks with infected avoidance strategy

In this paper, we study epidemic spreading on random surfer networks with infected avoidance(IA) strategy. In particular, we consider that susceptible individuals' moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However,when long-distance jumps of individuals exist, the IA strategy's effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive.